External Kink Research Articles

Feedback-assisted extension of the tokamak operating space to low safety factor

Recent DIII-D and RFX-mod experiments have demonstrated stable tokamak operation at very low values of the edge safety factor q(a) near and below 2. The onset of n = 1 resistive wall mode (RWM) kink instabilities leads to a disruptive stability limit, encountered at q(a) = 2 (limiter plasmas) and q95 = 2 (divertor plasmas). However, passively stable operation can be attained for q(a) and q95 values as low as 2.2. RWM damping in the q(a) = 2 regime was measured using active MHD spectroscopy. Although consistent with theoretical predictions, the amplitude of the damped response does not increase significantly as the q(a) = 2 limit is approached, in contrast with damping measurements made approaching the pressure-driven RWM limit. Applying proportional gain magnetic feedback control of the n = 1 modes has resulted in stabilized operation with q95 values reaching as low as 1.9 in DIII-D and q(a) reaching 1.55 in RFX-mod. In addition to being consistent with the q(a) = 2 external kink mode stability limit, the unstable modes have growth rates on the order of the characteristic wall eddy-current decay timescale in both devices, and a dominant m = 2 poloidal structure that is consistent with ideal MHD predictions. The experiments contribute to validating MHD stability theory and demonstrate that a key tokamak stability limit can be overcome with feedback.

Effect of passive structure and toroidal rotation on resistive wall mode stability in the EAST tokamak

If βN exceeds βNno—wall, the plasma will be unstable because of external kink and resistive wall mode (RWM). In this article, the effect of the passive structure and the toroidal rotation on the RWM stability in the experimental advanced superconducting tokamak (EAST) are simulated with CHEASE and MARS codes. A model using a one-dimensional (1D) surface to present the effect of the passive plate is proved to be credible. The no wall βN limit is about 3li, and the ideal wall βN limit is about 4.5li on EAST. It is found that the rotation near the q = 2 surface and the plasma edge affects the RWM more.

Physics and Control of External Kink Instabilities with Realistic 3D Boundaries: a Challenge for Modern Experiments and Modeling

Physics and Control of External Kink Instabilities with Realistic 3D Boundaries: a Challenge for Modern Experiments and Modeling

Measurement of 3D plasma response to external magnetic perturbations in the presence of a rotating external kink

The detailed measurements of the 3D plasma response to applied external magnetic perturbations in the presence of a rotating external kink are presented, and compared with the predictions of a single-helicity linear model of kink mode dynamics. The modular control coils of the High Beta Tokamak-Extended Pulse (HBT-EP) device are used to apply resonant m/n = 3/1 magnetic perturbations to wall-stabilized tokamak plasmas with a pre-existing rotating 3/1 kink mode. The plasma response is measured in high-resolution with the extensive magnetic diagnostic set of the HBT-EP device. The spatial structures of both the naturally rotating kink mode and the externally driven response are independently measured and observed to be identical, while the temporal dynamics are consistent with the independent evolution and superposition of the two modes. This leads to the observation of a characteristic change in 3D field dynamics as a function of the applied field amplitude. This amplitude dependence is found to be different for poloidal and radial fields. The measured 3D response is compared to and shown to be consistent with the predictions of the linear single-helicity model in the “high-dissipation” regime, as reported previously [M. E. Mauel et al., Nucl. Fusion 45, 285 (2005)].

Response of a partial wall to an external perturbation of rotating plasma

In this paper, we present the response of a 3D thin multiply connected wall to an external kink mode perturbation in axisymmetric tokamak configurations. To calculate the contribution of the plasma perturbed magnetic field in the vacuum region, we have made use of the concept of surface currents [following C. V. Atanasiu, A. H. Boozer, L. E. Zakharov, and A. A. Subbotin, Phys. Plasmas 6, 2781 (1999)]. The wall response is expressed in terms of a stream function of the wall surface currents, which are obtained by solving a diffusion type equation, taking into account the contribution of the wall currents themselves iteratively. The use of stream function makes the approach applicable for both well-studied earlier Resistive Wall Modes and for Wall Touching Kink Modes, which were discovered recently as a key phenomenon in disruptions [L. E. Zakharov, S. A. Galkin, and S. N. Gerasimov, Phys. Plasmas 19, 055703 (2012)]. New analytical expressions, suitable for numerical calculations of toroidal harmonics of the vacuum magnetic fields from the surface currents on axisymmetric shells, are derived.

Analysis of global hydromagnetic instabilities driven by strongly sheared toroidal flows in tokamak plasmas

Recent numerical calculations have shown that while strong toroidal rotation can increase the external kink limit of tokamak plasmas, the associated rotation shear can drive a Kelvin–Helmholtz like global instability in the plasma, if the rotation frequency exceeds a threshold value (Chapman et al 2011 Plasma Phys. Control. Fusion 53 125002; Chapman et al 2012 Nucl. Fusion 52 042005). On the basis of a large aspect ratio toroidal expansion of the magnetohydrodynamic stability equations, the present paper investigates analytically various properties of this instability in tokamak plasmas with sonic toroidal flows and low magnetic shear in the core region. We also compare the analytical results with numerical code calculations. Many characteristic features and parameter dependences of the instability can be understood from the analytical theory, such as an eigenmode structure peaking at the position of largest rotation shear, and insensitivity of the growth rate to the plasma beta and to the precise value of the safety factor in the region of low magnetic shear. From an algebraic expression for the growth rate, valid asymptotically at large rotation frequencies, the drop in the dynamic pressure associated with the flow in the plasma can be identified as a major driving mechanism of the instability. For modes with (dominant) poloidal mode number m > 1, and rotating equilibria with isothermal magnetic surfaces, another driving mechanism of the instability is related to the centrifugally induced density variation along the magnetic field lines.

Adaptive feedback control of rotating external kink modes in HBT-EP

An advanced adaptive control algorithm is used to study the control of external kink modes that are excited in the HBT-EP tokamak and have a natural toroidal rotation frequency near 8 kHz. The controller's system model is parametrized and the parameters are adjusted in real-time to match the measured plasma evolution. Depending upon a programmed phase angle, active feedback control is shown to either suppress or amplify the controlled amplitude by an amount comparable to the variations observed over a variety of plasma discharges. With negative feedback, the maximum amplitude is reduced to 40% of the uncontrolled value. With positive feedback, the amplitude increases to 155%. Intermediate feedback phases lead to an acceleration or deceleration of the mode rotation frequency in addition to changes in mode amplitude. As the feedback gain increases, the level of both mode suppression and mode amplification also increases. However, for sufficiently high gain, kink mode suppression becomes limited by the excitation of an additional, slowly rotating 1.4 kHz mode having the same helical structure as the uncontrolled kink. High gain amplification is limited by disruptive loss of plasma current. Experimental results are compared with numerical simulations based on a single helicity model, and qualitative agreement is found.

Multimode observations and 3D magnetic control of the boundary of a tokamak plasma

We present high-resolution detection and control of the 3D magnetic boundary in the High Beta Tokamak-Extended Pulse (HBT-EP) device. Measurements of non-axisymmetric radial and poloidal fields are made using 216 magnetic sensors positioned near the plasma surface. Control of 3D fields is accomplished using 40 independent saddle coils attached to the passive stabilizing wall. The control coils are energized with high-power solid-state amplifiers, and massively parallel, high-throughput feedback control experiments are performed using low-latency connections between PCI Express analogue input and output modules and a graphics processing unit. The time evolution of unstable and saturated wall-stabilized external kink modes are studied with and without applying magnetic perturbations using the control coils. The 3D dynamic structure of the magnetic field surrounding the plasma is determined through biorthogonal decomposition using the full set of magnetic sensors without the need to fit either a Fourier or a model-based basis. Naturally occurring external kinks are composed of multiple independent helical modes. Smooth transitions between dominant poloidal mode numbers are observed for simultaneous n = 1 and n = 2 modes as the edge safety factor changes. Relative amplitudes of coexistent m/n = 3/1 and 6/2 modes depend on the plasma's major radius and edge safety factor. When stationary 3/1 magnetic perturbations are applied, the resonant response can be linear, saturated, or disruptive, depending upon the perturbation amplitude and the edge safety factor; increased plasma–wall interactions from the perturbed plasma are proposed as a saturation mechanism. Initial feedback experiments have used 40 sensors and 40 control coils, producing mode amplification or suppression, and acceleration or deceleration depending on the feedback phase angle.

Tearing mode stability in a toroidally flowing plasma

The effect of a sheared toroidal equilibrium flow on the tearing mode stability index, Δ′, is studied. A flow modified external kink equation for a single helicity mode is derived in a toroidal geometry. The corrections to Δ′ arising from flow contributions are estimated on the basis of a boundary layer calculation. Toroidal shear flow is seen to have a destabilizing influence on the tearing mode in a manner similar to pure axial flows in a cylindrical geometry. However, the increase in Δ′ as a function of increasing flow is seen to be smaller than the cylindrical case due to beneficial magnetic curvature effects. Shear flow associated stabilization, as observed in many recent experiments, might be arising from other physical effects such as toroidal mode couplings which are neglected in the present model.

Error field assessment from driven rotation of stable external kinks at EXTRAP-T2R reversed field pinch

A new non-disruptive error field (EF) assessment technique not restricted to low density and thus low beta was demonstrated at the EXTRAP-T2R reversed field pinch. Stable and marginally stable external kink modes of toroidal mode number n = 10 and n = 8, respectively, were generated, and their rotation sustained, by means of rotating magnetic perturbations of the same n. Due to finite EFs, and in spite of the applied perturbations rotating uniformly and having constant amplitude, the kink modes were observed to rotate non-uniformly and be modulated in amplitude. This behaviour was used to precisely infer the amplitude and approximately estimate the toroidal phase of the EF. A subsequent scan permitted to optimize the toroidal phase. The technique was tested against deliberately applied as well as intrinsic EFs of n = 8 and 10. Corrections equal and opposite to the estimated error fields were applied. The efficacy of the error compensation was indicated by the increased discharge duration and more uniform mode rotation in response to a uniformly rotating perturbation. The results are in good agreement with theory, and the extension to lower n, to tearing modes and to tokamaks, including ITER, is discussed.

Physics of resistive wall modes

The advanced tokamak regime is a promising candidate for steady-state tokamak operation which is desirable for a fusion reactor. This regime is characterized by a high bootstrap current fraction and a flat or reversed safety factor profile, which leads to operation close to the pressure limit. At this limit, an external kink mode becomes unstable. This external kink is converted into the slowly growing resistive wall mode (RWM) by the presence of a conducting wall. Reduction of the growth rate allows one to act on the mode and to stabilize it. There are two main factors which determine the stability of the RWM. The first factor comes from external magnetic perturbations (error fields, resistive wall, feedback coils, etc). This part of RWM physics is the same for tokamaks and reversed field pinch configurations. The physics of this interaction is relatively well understood and based on classical electrodynamics. The second ingredient of RWM physics is the interaction of the mode with plasma flow and fast particles. These interactions are particularly important for tokamaks, which have higher plasma flow and stronger trapped particle effects. The influence of the fast particles will also be increasingly more important in ITER and DEMO which will have a large fraction of fusion born alpha particles. These interactions have kinetic origins which make the computations challenging since not only particles influence the mode, but also the mode acts on the particles. Correct prediction of the ‘plasma–RWM’ interaction is an important ingredient which has to be combined with external field's influence (resistive wall, error fields and feedback) to make reliable predictions for RWM behaviour in tokamaks. All these issues are reviewed in this paper.

High resolution detection and excitation of resonant magnetic perturbations in a wall-stabilized tokamak

We report high-resolution detection of the 3D plasma magnetic response of wall-stabilized tokamak discharges in the High Beta Tokamak-Extended Pulse [T. H. Ivers et al., Phys. Plasmas 3, 1926 (1996)] device. A new adjustable conducting wall has been installed on HBT-EP made up of 20 independent, movable, wall segments instrumented with three distinct sets of 40 modular coils that can be independently driven to generate a wide variety of magnetic perturbations. High-resolution detection of the plasma response is made with 216 poloidal and radial magnetic sensors that have been located and calibrated with high-accuracy. Static and dynamic plasma responses to resonant and non-resonant magnetic perturbations are observed through measurement of the step-response following a rapid change in the toroidal phase of the applied perturbations. Biorthogonal decomposition of the full set of magnetic sensors clearly defines the structures of naturally occurring external kinks as being composed of independent m/n = 3/1 and 6/2 modes. Resonant magnetic perturbations were applied to discharges with pre-existing, saturated m/n = 3/1 external kink mode activity. This m/n = 3/1 kink mode was observed to lock to the applied perturbation field. During this kink mode locked period, the plasma resonant response is characterized by a linear, a saturated, and a disruptive plasma regime dependent on the magnitude of the applied field and value of the edge safety factor and plasma rotation.

Understanding disruptions in tokamaks

This paper describes progress achieved since 2007 in understanding disruptions in tokamaks, when the effect of plasma current sharing with the wall was introduced into theory. As a result, the toroidal asymmetry of the plasma current measurements during vertical disruption event (VDE) on the Joint European Torus was explained. A new kind of plasma equilibria and mode coupling was introduced into theory, which can explain the duration of the external kink 1/1 mode during VDE. The paper presents first results of numerical simulations using a free boundary plasma model, relevant to disruptions.

Kinetic effects of trapped energetic particles on stability of external kink modes with a resistive wall

Kinetic effects of trapped energetic particles (EPs) on stability of the external kink mode with a resistive wall are investigated in detail, on the basis of the theory model developed in a previous paper [G. Z. Hao, A. K. Wang, Y. Q. Liu, and X. M. Qiu, Phys. Rev. Lett. 107, 015001 (2011)]. The results indicate that, when the perpendicular beta β* of the trapped EPs exceeds a critical value βc*, a bursting fishbone-like mode (FLM) instability, with external kink eigenstructure ,can be triggered, which rapidly grows with increasing β*(>βc*), and eventually becomes a dominant instability. Detailed physical analyses are carried out, comparing radial profiles of the EPs kinetic energy for both the FLM and the conventional resistive wall mode (RWM). On the other hand, a mode conversion between the FLM and RWM can directly occur. This work also presents a systematic investigation of effects of various physical parameters on the FLM instability. An interesting new finding is the existence of multiple critical points in β*, for the FLM triggering. The number of critical points depends sensitively on the trapped EPs pitch angle. In addition, it is found that there can be a critical value of the pitch angle, beyond which the critical βc*, for triggering the FLM, jumps from a large value to a small one. The FLM instability, with the m/n=3/1 mode structure, can also be triggered by the trapped EPs.

Kinetic versus ideal magnetohydrodynamic modelling of the resistive wall mode in a reversed field pinch plasma

Resistive wall modes (RWMs) are studied within the kinetic model proposed by Heyn et al. [Nucl. Fusion 46, S159 (2006); Phys. Plasmas 18, 022501 (2011)], which accounts for Landau damping, transit-time magnetic pumping, and Coulomb collisions in cylindrical geometry. Results for the reversed field pinch plasma are compared to the magnetohydrodynamic results obtained by Guo et al., [Phys. Plasmas 6, 3868 (1999)]. Stabilization of the external kink mode by an ideal wall as well as stabilization of the resistive wall mode by toroidal plasma rotation is obtained. In contrast to MHD modelling, which predicts a stability window for the resistive wall position, kinetic modelling predicts a one sided window only, i.e., the resistive wall must be sufficiently close to plasma to achieve rotational stabilization of the mode but there is no lower limit on the wall position. Stabilizing rotation speeds are found somewhat smaller when compared to MHD results. In addition, for the present plasma configuration, the kinetic model predicts resistive wall mode stabilization only in one direction of toroidal rotation. In the opposite direction, a destabilizing effect is observed. This is in contrast to MHD where mode stabilization is symmetric with respect to the direction of the toroidal plasma rotation.

Feedback control of the proximity to marginal RWM stability using active MHD spectroscopy

DIII-D experiments yield the first proof-of-principle results in feedback control of the proximity to the resistive wall mode (RWM) stability boundary using an active MHD spectroscopic stability measurement and neutral beam injection heating. In contrast to calculations of the stability of reconstructed equilibria, the spectroscopic measurement is independent of the assumed RWM stability model. The real-time implementation enables the control system to react to unforeseen changes in plasma parameters and hence stability limits. In the experimentally accessed regime, near but below the ideal-MHD no-wall limit for the n = 1 external kink instability, the control dynamics are described by a linear model that depends on the plasma stored energy. This model is used to aid in optimizing feedback gain settings.

The effects of sheared toroidal rotation on stability limits in tokamak plasmas

Sheared toroidal rotation is found to increase the ideal external kink stability limit, thought to be the ultimate performance limit in fusion tokamaks. However, at rotation speeds approaching a significant fraction of the Alfvén speed, the toroidal rotation shear drives a Kelvin–Helmholtz-like global plasma instability. Optimizing the rotation profile to maximize the pressure before encountering external kink modes, but simultaneously avoiding flow-driven instabilities, can lead to a window of stability that might be attractive for operating future high-performance fusion devices such as a spherical tokamak component test facility.

Experimental verification of the Kruskal-Shafranov stability limit in line-tied partial-toroidal plasmas

The stability properties of partial-toroidal flux ropes are studied in detail in the laboratory, motivated by ubiquitous arched magnetic structures found on the solar surface. The flux ropes studied here are magnetized arc discharges formed between two electrodes in the Magnetic Reconnection Experiment (MRX) [Yamada et al., Phys. Plasmas 4, 1936 (1997)]. The three dimensional evolution of these flux ropes is monitored by a fast visible light framing camera, while their magnetic structure is measured by a variety of internal magnetic probes. The flux ropes are consistently observed to undergo large-scale oscillations as a result of an external kink instability. Using detailed scans of the plasma current, the guide field strength, and the length of the flux rope, we show that the threshold for kink stability is governed by the Kruskal-Shafranov limit for a flux rope that is held fixed at both ends (i.e., qa = 1).

Geometry, microstructures, and magnetic fabrics of kink bands in the Darrington Phyllite, northwestern Washington, USA: Processes within fixed-hinge kinking

Field, thin section, and magnetic fabric analyses of monoclinal, contractional kink bands in the Darrington Phyllite of northwestern Washington, USA, provide evidence of kinematic evolution and microstructural processes during kinking. Relationships among internal, external, and rotation angles of kink bands suggest that rotation was a primary mechanism of kinking, and a significant number of kink bands deviate from the “ideal” kink band geometry (equal internal and external kink angles). Dilation spaces (voids) filled with unrecrystallized quartz and/or calcite inside kink bands and along the boundaries are commonly observed in kink bands with unequal kink angles. Evidence for localized interlayer slip inside kink bands includes mica grains protruding into the hinge voids and stair-step geometry of the voids. Interlayer slip allowed for rotation of the internal foliation during kinking. Pressure solution is not ubiquitous inside kink bands from the study area; however, significant pressure solution is associated with “locked” kink bands (equal kink angles). A new approach using the anisotropy of magnetic susceptibility (AMS) shows that the magnetic fabric and susceptibility inside the kink bands differ more from the outside fabric than can be explained by simple rotation of the outside fabric into the kink attitudes. Combined, our observations suggest that fixed-hinge kinking operated at this location, and that veining, interlayer slip, and pressure solution were the dominant deformation mechanisms.

High spatial sampling global mode structure measurements via multichannel reflectometry in NSTX

Global modes—including kinks and tearing modes (f <∼ 50 kHz), toroidicity-induced Alfvén eigenmodes (TAE; f ∼ 50–250 kHz) and global and compressional Alfvén eigenmodes (GAE and CAE; f >∼ 400 kHz)—play critical roles in many aspects of plasma performance. Their investigation on NSTX is aided by an array of fixed-frequency quadrature reflectometers used to determine their radial density perturbation structure. The array has been recently upgraded to 16 channels spanning 30–75 GHz (ncutoff = (1.1–6.9) × 1019 m−3 in O-mode), improving spatial sampling and access to the core of H-mode plasmas. The upgrade has yielded significant new results that advance the understanding of global modes in NSTX. The GAE and CAE structures have been measured for the first time in the core of an NSTX high-power (6 MW) beam-heated H-mode plasma. The CAE structure is strongly core-localized, which has important implications for electron thermal transport. The TAE structure has been measured with greatly improved spatial sampling, and measurements of the TAE phase, the first in NSTX, show strong radial variation near the midplane, indicating radial propagation caused by non-ideal MHD effects. Finally, the tearing mode structure measurements provide unambiguous evidence of coupling to an external kink.